Geodesic
Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion
John W. Barrett1 ; Klaus Deckelnick2
1Imperial College London, United Kingdom
2Otto-von-Guericke-Universität Magdeburg, Germany
Interfaces and free boundaries, Tome 14 (2012) no. 3, pp. 343-363

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DOI

We consider a nonlinear parabolic system of reaction–diffusion equations modelling acid-mediated tumour invasion. The system couples potentially degenerate equations for the cell densities of the normal and tumour populations to a parabolic equation for the concentration of HC ions. We obtain an existence result for the system by constructing a suitable finite element approximation and analyzing its convergence. Finally, we report on corresponding numerical experiments.
DOI : 10.4171/ifb/284
Classification : 35-XX, 65-XX, 00-XX
Mots-clés : Degenerate parabolic system, porous medium equation, existence, finite elements, tumour invasion

John W. Barrett  1   ; Klaus Deckelnick  2

1 Imperial College London, United Kingdom
2 Otto-von-Guericke-Universität Magdeburg, Germany 
John W. Barrett; Klaus Deckelnick. Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion. Interfaces and free boundaries, Tome 14 (2012) no. 3, pp. 343-363. doi: 10.4171/ifb/284
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